Gottstein G., Shvindlerman L.S. Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications

Подождите немного. Документ загружается.

546 6 Applications

(a)

(b)

(c)

(d)

FIGURE 6.27

Rolling and recrystallization textures of Cube metals in {111} pole ﬁgure and

Euler space. (a) Cu-type rolling texture; (b) brass-type rolling texture; (c)

Cube texture (Cu-recrystallization texture); (d) brass recrystallization tex-

ture.

6.2 Recrystallization annd Grain Growth 547

{110} R D

levels: 0.5

MAX = 6.3

= const.

FUNE ODF

MAX = 35.6

levels:

2 4 7 12

20 30

MAX = 35.6

levels:

2 4 7 12

= const.

FUNE ODF

{110} R D Levels: 0.5

MAX = 10.3

fibre

(a)

(b)

(c)

fibre

(011)[100]

(001)[100] α

fibre

(110)[001]

(001)[

110

]

(111)[

110

]

(001)[

110

]

(111)[

121

]

(111)[

112

]

(111)[

011

]

(112)[

111

]

(011)[

211

]

(011)[

011

]

(001)[

(112)[

(110)[

(111)[

(112)[

(110)[

(001)[

110

]

110

]

112

111

110

00 1

112

]

110

010

]

fibre

<001> II ND

= 45°

<111> II ND

<110> II RD

<110> II TD

FIGURE 6.28

Rolling and recrystallization texture of bcc metals (ferritic steel). (a) {110}

pole ﬁgure, and ODF in 3D and sectional Euler space of rolling texture; (b)

{110} pole ﬁgure and ODF in Euler space; (c) location of ﬁbers in Euler space

that contain the main texture components. The ϕ

=45

◦

sections contain the

most information.

548 6 Applications

6.2.4.2 Pure Metals: Growth Selection

In such experiments a single crystal is slightly deformed, for instance by

rolling. If the orientation of the single crystal does not change or decompose

during deformation, the deformed specimen still represents a single crystal

but with a stored energy of cold work in terms of the elastic energy of the

stored dislocations. After deformation, one face of the single crystal will be

subjected to an additional strong deformation, e.g. by grinding, ﬁling or saw-

ing. Afterwards the sample is annealed in a strong temperature gradient, such

that only a small volume of the sample is heated while the remaining deformed

volume is kept at ambient temperature (Fig. 6.29). Annealing starts at the

additionally deformed end, giving rise to a high nucleation density with vir-

tually random orientation distribution. These nuclei grow upon displacement

of the hot zone and compete with one another such that the fastest growing

grains will cut oﬀ the path of the more slowly growing grains, and eventually

a single grain will dominate and cover the entire cross section of the consumed

single crystal. Obviously, this ﬁnal surviving grain will be the fastest (max-

imum growth rate orientation), and the grain boundary between this grain

and the deformed single crystal possesses the highest mobility among all com-

peting grain boundaries. Of course, a single experiment might give incidental

results. However, hundreds of experiments were conducted on high purity Al

with the overwhelming result that grains with a 40

◦

111 orientation rela-

tionship to the deformed matrix evidently grew fastest. Naturally, there is a

certain statistical distribution of fast-growing orientations. However, the fur-

ther the competing grains proceed into the consumed deformed single crystal,

the sharper the distribution of misorientation angles (Fig. 6.29).

According to such experiments, the maximum of the distribution is attained

at an angle slightly above 40

◦

about a 111 axis. In the past, the high mobil-

ity of 40

◦

111 boundaries was interpreted such that the 40

◦

111 boundary

actually represented a 38.2

◦

111 Σ7 coincidence boundary [394, 587]. Owing

to the high density of coincidence sites the boundary would segregate less so-

lute atoms than other boundaries and thus be less aﬀected by impurity drag.

Less impurity drag is equivalent to a higher eﬀective driving force and thus

higher growth rate. In fact, the orientation dependence of grain boundary mo-

bility measured for the individual grain boundaries proved that low Σ CSL

boundaries (special boundaries) behaved in a more mobile way than random

boundaries (non-special boundaries), and among all boundaries with low in-

dex rotation axes the Σ7 boundary moved fastest (see Chapter 3). However,

the maximum growth rate misorientation is distinctly diﬀerent from the Σ7

orientation relationship, and always larger by at least 2 degrees. Thus, the

interpretation given above obviously is at variance with the results of growth

selection experiments. A more detailed analysis reveals the reason for the dis-

crepancy. The Σ7 boundary indeed moves fastest at temperatures below 430

◦

(Fig. 6.30) while at higher temperatures the 40.5

◦

111 boundary exhibits the

highest mobility. Given the fact that the temperature during growth selection

6.2 Recrystallization annd Grain Growth 549

cut

region

NNN N

stage I

stage II stage III

stage I

stage II

stage III

140° 150° 160° 170°

rotation angle

(a) (b)

FIGURE 6.29

(a) Principle of growth selection; (b) {111} pole ﬁgures and frequency distri-

bution of the orientations still in contact with the deformed matrix for three

consecutive stages of growth selection ([586]).

experiments is very high, typically above 600

◦

C for Al, it is evident that such

experiments are designed to reveal a 40

◦

111 misorientation as maximum

growth rate (mis)orientation rather than the Σ7 misorientation (Fig. 6.31).

The physical principle that creates this confusion is the compensation ef-

fect discussed at length in Chapter 3. At temperatures below the compen-

sation temperature T

the process with the lower activation enthalpy will

dominate, while above T

such mechanisms are favored that carry the largest

pre-exponential factor (Fig. 6.32). It is noted that this result reveals a com-

mon misconception, namely that the process with the lower activation en-

thalpy will always be favored, tacitly assuming that the pre-exponential factor

hardly varies, which is obviously wrong. The widely practiced habit to ana-

lyze thermally activated processes only with regard to the activation enthalpy

is, therefore, liable to serious misinterpretation. This is particularly true for

interfacial phenomena, where the activation enthalpy varies in a wide range.

For instance, if only the activation enthalpy would diﬀer for the mobility of

dissimilar (large angle) boundaries, the mobilities would diﬀer by many or-

ders of magnitude, while in reality the mobility of grain boundaries varies only

within a factor of ten or so.

550 6 Applications

430°C

485°C

540°C

-7

-8

-9

A [m

/s]

36 38 40 42 44

[deg]

430°C

485°C

540°C

FIGURE 6.30

Dependence of the reduced mobility of 111 tilt grain boundaries on rotation

angle in pure Al at diﬀerent temperatures.

T=615°C

T = 615°C

A [

/s]

36° 37° 38° 39° 40° 41° 42° 43° 44°

misorientation

FIGURE 6.31

Reduced mobility of investigated 111 tilt grain boundaries in Al at 615

◦

(obtained by extrapolation of the measured temperature dependence to

615

◦

C).

6.2 Recrystallization annd Grain Growth 551

38.2°<111>

40.5°<111>

550 500 450

T [°C]

-6

-7

-8

-9

-10

1.2

A [m

/s]

1.25 1.3

1.35

1.4 1.45

40.5° <111>

38.2° <111>

1/T [10

/K]

FIGURE 6.32

Temperature dependence of the reduced mobility A for 38.2

◦

and 40.5

◦

111

tilt grain boundaries in pure Al.

6.2.4.3 Growth-Controlled Recrystallization Textures

Growth selection experiments on pure aluminum have clearly established the

high growth rate of 40

◦

111 tilt boundaries in this material. Its importance

for microstructure development, however, derives from the fact that the main

components of the recrystallization textures of rolled Al (Cube texture) can be

related to the major rolling texture components (S-orientation) by a 40

◦

111

orientation relationship (Fig. 6.33). This constitutes the basis of the so-called

“theory of oriented growth” which contends that the recrystallization texture

forms from (tacitly assumed) randomly oriented nuclei by growth selection in

favor of maximum growth rate orientations, i.e. 40

◦

111. There have been

reﬁnements to this approach to account for obvious discrepancies from ideal

◦

111 rotations, in particular the compromise texture approach, which de-

mands that a growing grain be able to grow quickly into more than a single

component of the rolling texture (Fig. 6.33) [583]. More reﬁned modeling ap-

proaches [588] and computer simulations [589] have conﬁrmed that a growth

preference of a 40

◦

111 rotation leads to the observed recrystallization tex-

tures. The inﬂuence of a growth advantage is so strong that other compromise

◦

111 rotations are completely suppressed even if their compromise ﬁt is

marginally less perfect. This would explain why other potential recrystalliza-

tion texture components were never observed.

Other approaches also have been put forward recently to explain the dom-

inance of the 40

◦

111 misorientation, even in the absence of an orientation-

dependent growth rate. Besides the classical contention of oriented nucleation,

552 6 Applications

R D

S (left) and Cube (right) with 40° <111> rotations of S

R D

= Bs-texture

{}011 21 1

= Bs-recrystallization texture

{236}

385

~40°

{111}

Bs (left) and Bs/R (right) with 40° <111> rotations of Bs

(a)

(b)

(c)

FIGURE 6.33

Orientation relationship between rolling and recrystallization texture compo-

nents. (a) The Cube texture satisﬁes a best ﬁt of a 40

◦

111 rotation of the

S orientation; (b) the brass recrystallization texture is related to the brass

rolling texture by a 40

◦

111 rotation; (c) illustration of the orientation rela-

tionship for one brass rolling and recrystallization component.

6.2 Recrystallization annd Grain Growth 553

i.e. the preferential nucleation of major recrystallization texture components,

e.g. the Cube texture in aluminum, an eﬀect of orientation pinning recently

was proposed [590]. Orientation pinning relates to the experimental obser-

vation that small angle boundaries (and coherent twin boundaries) have low

mobility and can be considered as essentially sessile. While it is diﬃcult to

completely block a grain boundary in three dimensions this concept also can-

not satisfactorily account for the observed recrystallization textures [591], al-

though it ampliﬁes selective growth and thus perhaps another reason for the

observed sharp recrystallization textures in aluminum alloys.

A truly surprising phenomenon is that the selective growth, which was

unambiguously evidenced in pure Al, can also account for recrystallization

texture formation in other metals and alloys, even intermetallic compounds.

For instance, the recrystallization texture of Cu-30%Zn (α−brass) can be

successfully predicted by assuming a compromise texture of 40

◦

111 rota-

tions (Fig. 6.33) [592]]. This is remarkable, since the deformation structure

and the recrystallized microstructure of brass are entirely diﬀerent from the

deformed and recrystallized state of Al, namely heavily twinned and shear

banded after rolling as well as ﬁne-grain sized and massively twinned after

recrystallization. The major problem of relating the recrystallization texture

to the rolling texture in brass is the fact that not all theoretically predicted

compromise orientations appear in the experimental recrystallization texture.

This problem can be mitigated by twin formation as an additional selective

nucleation process [593].

Forcopperandsilvera30

◦

111 rotation seems to more appropriately de-

scribe the maximum growth rate orientation, as evident from recrystallization

experiments on single crystals. Growth selection experiments are more diﬃcult

to conduct for these materials, since repeated annealing twin formation gen-

erates high-order twin families, which interfere with the growth process such

that usually more than a single grain survives growth competition [594]. Nev-

ertheless, the grains surviving growth selection can be associated with some

scatter to a 30

◦

111 orientation relationship between growing grain and con-

sumed deformed matrix. To reconcile the results on Al with observations on

other fcc materials, reference usually is made to a 30

◦

− 40

◦

111 rotation.

This is, however, incorrect, as shown by very detailed investigations on Al and

can only be tolerated in view of the lack of reliable data on materials other

than Al.

The dominance of 40

◦

111 rotations is truly remarkable. If an Al single

crystal is deformed such that the spread of the orientation will slightly favor

the occurrence of only a single variant of all possible eight ±40

◦

111rotations,

then the recrystallization texture consists of only one component (Fig. 6.34),

namely this variant, despite the fact that there are many other orientations

present in the orientation spread of the deformed matrix [595, 596]. Even more

surprising is the recrystallization texture of deformed single crystals with a

stable orientation during rolling. The recrystallization texture comprises ex-

actly all eight ±40

◦

111 rotations of the rolled single crystal orientation,

554 6 Applications

TTT

deformation texture orientation relationshipsrecrystallization texture

SA SA SA

CD CD CD

(a)

(b)

FIGURE 6.34

{111} pole ﬁgures of deformed and recrystallized Al single crystals (according

to [596]). (a) 112 crystals, tensile deformed 50%; (b) (2.1.10)[42

1] crystal,

80% rolled.

irrespective of whether it is aluminum, brass [593] or even the intermetallic

compound Ni

Al (Fig. 6.35) [597]. The latter case is particularly surprising,

since rolled Ni

Al polycrystals exhibit only a very weak recrystallization tex-

ture, and it is generally assumed that long-range order strongly reduces grain

boundary mobility and thus eliminates a particular orientation dependence of

grain boundary mobility.

Recently, Hutchinson [598] proposed attributing the observed frequency of

◦

111 rotations to a special property of a random misorientation distri-

bution. When a random misorientation distribution is sorted into rotations

about low index rotation axes, e.g. 111 rotation axes, allowing for a devi-

ation of about 15

◦

, the corresponding angular misorientation distribution is

not random but peaks at an angle of about 30

◦

, similar to growth selection

experiments; however, this result has to be treated with caution. In growth

selection experiments it is determined which orientation grows into a speciﬁc

(single crystal) orientation. If this growth would be orientation independent

then the distribution of successful grains ought to represent the orientation

distribution itself and not the misorientation distribution. Besides, the com-

puted angular misorientation distribution is distinctly diﬀerent from growth

selection results on Al, and the results of mobility measurements on individ-

ual grain boundaries in Al prove an orientation dependence of grain boundary

6.2 Recrystallization annd Grain Growth 555

111

(a)

R D LEVELS:

KO801

MAX= 35.1

111

R D

LEVELS:

MAX= 8.6KO803

R D

111

LEVELS: 1

MAX= 8.4SO8010

(b)

FIGURE 6.35

(a) {111} pole ﬁgure of rolling and recrystallization texture of a (617)3.10.

4

single crystal of Ni

Al; (b) the recrystallization texture comprises all eight

±35

◦

111 rotations of the single crystal orientation.